The excellence in the approximation of the solution
of GR does not necessarily mean the stability of this solution. In
general, providing the stability of a gravitational solution under
arbitrary small perturbations (that do not have the symmetry
of solutions themselves) may be not simple even in GR, for some
gravitational backgrounds. Let us mention, for instance, the study
of the stability of the Schwarzschild solution in GR [1]}, [2]}
(see also [3]}).
In the presence of \(C^2\)  term, one can expect that the same solution
will not be stable. Regardless of existing contradictions in the
literature, in general, this expectation is confirmed [4]}, [5]}.
Owing to the high level of technical difficulty, this case will not be
discussed here.
